The table lists the drinking habits of a group of college students.  If a student is chosen at random, find the probability of getting someone who is a man or a non-drinker. Round your answer to three decimal places.

Sex	Non-drinker 	Regular Drinker	Heavy Drinker	Total 
Man	135	47	5	187
Woman	187	21	7	215
Total	322	68	12	402


To find the probability of selecting someone who is a man or a non-drinker, we will use the following formula for the probability of "A or B" occurring (for mutually non-exclusive events):

\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\]

Where:
- \( P(A) \) is the probability of selecting a man.
- \( P(B) \) is the probability of selecting a non-drinker.
- \( P(A \text{ and } B) \) is the probability of selecting someone who is both a man and a non-drinker.

### Step 1: Calculate \( P(A) \) (Probability of selecting a man)
\[
P(A) = \frac{\text{Number of men}}{\text{Total number of students}} = \frac{187}{402}
\]

### Step 2: Calculate \( P(B) \) (Probability of selecting a non-drinker)
\[
P(B) = \frac{\text{Number of non-drinkers}}{\text{Total number of students}} = \frac{322}{402}
\]

### Step 3: Calculate \( P(A \text{ and } B) \) (Probability of selecting someone who is both a man and a non-drinker)
\[
P(A \text{ and } B) = \frac{\text{Number of men who are non-drinkers}}{\text{Total number of students}} = \frac{135}{402}
\]

### Step 4: Apply the formula for \( P(A \text{ or } B) \)
\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\]
Substitute the values:
\[
P(A \text{ or } B) = \frac{187}{402} + \frac{322}{402} - \frac{135}{402}
\]

### Step 5: Simplify the expression
\[
P(A \text{ or } B) = \frac{187 + 322 - 135}{402} = \frac{374}{402} \approx 0.930
\]

So, the probability of selecting someone who is a man or a non-drinker is approximately **0.930**.

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Would you like any further details or clarifications?

Here are 5 related questions to extend your understanding:
1. What is the probability of selecting a heavy drinker?
2. How would the probability change if you added another 100 women who are non-drinkers?
3. What is the probability of selecting someone who is a regular drinker and a woman?
4. If two students are selected randomly, what is the probability that both are men?
5. How do mutually exclusive and non-mutually exclusive events affect probability calculations?

**Tip**: When dealing with "or" probabilities, always remember to subtract the overlap between the two events to avoid double-counting!

The table lists the drinking habits of a group of college students. If a student is chosen at random, find the probability of getting someone who is a man or a non-drinker. Round your answer to three decimal places.

Find the probability of randomly selecting a man or a non-drinker from a table of drinking habits among college students. Learn how to apply the addition rule for non-mutually exclusive events using the given data. The solution includes step-by-step calculations and key probability concepts, suitable for high school students (Grades 10-12).

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